This paper discusses design and performance aspects of Twentenet, one of the few implemented LANs which offers a service based on message priorities. The medium access mechanism uses the CSMA/CD principle, however with a deterministic collision resolution method. These characteristics make Twentenet suitable for real-time applications, as well as a mixture of real-time and non real-time applications. The general system structure is introduced followed by a detailed description of the priority access method. The performance of the system is shown for various traffic conditions and distributions of message priorities. The effect of system parameters, such as transmission rate, message length, cable length, and retry limits, is indicated.